Probability matching and strategy availability

Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought to their attention, more participants subsequently engage in maximizing. Third, matchers are more likely than maximizers to base decisions in other tasks on their initial intuitions, suggesting that they are more inclined to use a choice strategy that comes to mind quickly. These results indicate that a substantial subset of probability matchers are victims of “underthinking” rather than “overthinking”: They fail to engage in sufficient deliberation to generate a superior alternative to the matching strategy that comes so readily to mind.     

Banking on a bad bet. Probability matching in risky choice is linked to expectation generation

Probability matching is the tendency to match choice probabilities to outcome probabilities in a binary prediction task. This tendency is a long-standing puzzle in the study of decision making under risk and uncertainty, because always predicting the more probable outcome across a series of trials (maximizing) would yield greater predictive accuracy and payoffs. In three experiments, we tied the predominance of probability matching over maximizing to a generally adaptive cognitive operation that generates expectations regarding the aggregate outcomes of an upcoming sequence of events. Under conditions designed to diminish the generation or perceived applicability of such expectations, we found that the frequency of probability-matching behavior dropped substantially and maximizing became the norm.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

Attention in risky choice

Previous research on the processes involved in risky decisions has rarely linked process data to choice directly. We used a simple measure based on the relative amount of attentional deployment to different components (gains/losses and their probabilities) of a risky gamble during the choice process, and we related this measure to the actual choice. In an experiment we recorded the decisions, decision times, and eye movements of 80 participants who made decisions on 11 choice problems. We used the number of eye fixations and fixation transitions to trace the deployment of attention during the choice process and obtained the following main results. First, different components of a gamble attracted different amounts of attention depending on participants' actual choice. This was reflected in both the number of fixations and the fixation transitions. Second, the last-fixated gamble but not the last-fixated reason predicted participants' choices. Third, a comparison of data obtained with eye tracking and data obtained with verbal protocols from a previous study showed a large degree of convergence regarding the process of risky choice. Together these findings tend to support dimensional decision strategies such as the priority heuristic.     

风险决策和跨期决策的过程比较：以确定效应和即刻效应为例

风险决策和跨期决策与人类生存发展密切相关, 且两类决策在理论发展、行为效应及神经基础等方面具有相似性。为检验二者是否具有共同过程机制, 本研究以风险决策中的确定效应和跨期决策中的即刻效应为例, 采用眼动追踪技术比较了它们的局部、整体过程及模型拟合。辅以贝叶斯因子分析实验数据表明：二者的主要过程特征均相似, 且更符合非折扣模型假设; 二者在加工复杂程度等少数特征上有所不同; 确定和即刻信息在加工方向等特征上存在特异性。这表明二者可能具有共同的核心决策规则：两类决策更可能遵循非折扣模型预期的简捷、启发式规则, 而不是折扣模型所假设的补偿性、基于选项规则。本研究为建立两类决策的共同解释框架做出了有益尝试, 并为决策比较研究方法提供新的方向。     

Decision by sampling: The role of the decision environment in risky choice

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts.     

The effect of time pressure on risky choice behavior

Thirty six subjects chose individually between pairs of gambles under three time pressure conditions: High (8 seconds), Medium (16 seconds) and Low (32 seconds). The gambles in each pair were equated for expected value but differed in variance, amounts to win and lose and their respective probabilities. Information about each dimension could be obtained by the subject sequentially according to his preference.The results show that subjects are less risky under High as compared to Medium and Low time pressure, risk taking being measured by choices of gambles with lower variance or lower amounts to lose and win. Subjects tended to spend more time observing the negative dimensions (amount to lose and probability of losing), whereas under low time pressure they preffered observing their positive counterparts. Information preference was found to be related to choices.Filtration of information and acceleration of its processing appear to be the strategies of coping with time pressure.     

Social cues and verbal framing in risky choice

We examined how people use social and verbal cues of differing priorities in making social decisions. In Experiment 1, formally identical life – death choice problems were presented in different hypothetical group contexts and were phrased in either a positive or negative frame. The risk‐seeking choice became more dominant as the number of kin in an endangered group increased. Framing effects occurred only in a heterogeneous group context where the lives at risk were a mixture of kin and strangers. No framing effect was found when the same problem was presented in the context of a homogeneous group consisting of either all kin or all strangers. We viewed the framing effects to be a sign of indecisive risk preference due to the differential effects of a kinship cue and a stranger cue on choice. In Experiment 2, we presented the life – death problem in two artificial group contexts involving either 6 billion human lives or 6 billion extraterrestrial lives. A framing effect was found only in the human context. Two pre‐conditions of framing effects appear to be social unfamiliarity of a decision problem and aspiration level of a decision maker. In Experiment 3, we analyzed the direction of the framing effect by balancing the framing. The direction of the framing effect depended on the baseline level of risk preference determined by a specific decision context. Copyright © 2001 John Wiley & Sons, Ltd.     

Forward inference in risky choice: Mapping gaze and decision processes

The study of cognitive processes is built on a close mapping between three components: overt gaze behavior, overt choice, and covert processes. To validate this overt–covert mapping in the domain of decision‐making, we collected eye‐movement data during decisions between risky gamble problems. Applying a forward inference paradigm, participants were instructed to use specific decision strategies to solve those gamble problems (maximizing expected values or applying different choice heuristics) during which gaze behavior was recorded. We revealed differences between overt behavior, as indicated by eye movements, and covert decision processes, instructed by the experimenter. However, our results show that the overt–covert mapping is for some eye‐movement measures not as close as expected by current decision theory, and hence question reverse inference as being prone to fallacies due to a violation of its prerequisite, that is, a close overt–covert mapping. We propose a framework to rehabilitate reverse inference.     

睡眠剥夺影响风险决策的双系统模型探讨

睡眠剥夺是指由于环境或自身原因无法满足正常睡眠时间的情况。大量实证研究发现, 睡眠剥夺会导致个体在风险决策中更倾向于风险寻求, 同时也有研究表明睡眠剥夺会导致个体风险规避, 而目前尚无统一结论。睡眠剥夺从风险感知、风险容忍、风险决策策略三个方面影响了风险决策, 其心理机制可由认知和情绪双路径模型进行解释, 且脑神经生理学研究也提供了相关证据。未来的研究应该进一步关注：(1)现实工作生活中的睡眠不足对风险决策的影响; (2)睡眠剥夺影响风险决策的理论模型建构。     

Self‐framing of risky choice

Previous research on framing effects has largely focused on how choice information framed by external sources influences the response of a decision maker. This research examined how decision makers framed choice options and how the hedonic tone of self‐framing influenced their risk preference. By using pie charts and a complementary sentence‐completion task in Experiment 1, participants were able to interpret and frame the expected choice outcomes themselves before making a choice between a sure option and a gamble in either a life–death or a monetary problem. Each of these self‐frames (phrases) was then rated by a group of independent judges in terms of its hedonic tone. The hedonic tone of self‐frames was mostly positive and was more positive in the life–death than the monetary context, suggesting a motivational function of self‐framing. However, positive outcomes were still more likely to be framed positively than negative outcomes. In Experiment 2, choice outcomes were depicted with a whole‐pie chart instead of a pie slice in order to emphasize positive and negative outcomes equally. The results showed that the hedonic tone of self‐framing was still largely positive and more positive in the life domain than the monetary domain. However, compared to Experiment 1, the risk preference in the life–death domain was reversed, showing an outcome salience effect: when the pie‐slice chart emphasized only survival outcomes, participants were more risk taking under positive hedonic frames whereas when the whole‐pie chart depicted both survival and mortality outcomes, they became risk averse under positive frames. In sum, self‐framing reflected a positive bias in encoding risk information and affected the risk preference of the decision maker. Like the tone of voice used in communication, the hedonic tone of self‐framing, either positive or negative, can affect risk perception of a choice problem. Copyright © 2003 John Wiley & Sons, Ltd.     

风险决策的概率权重偏差：心理机制与优化策略

概率权重偏差指人对事件发生的主观概率估计与客观概率的差异。它影响投资、投保、医患沟通等方面。“重结果轻概率”的非补偿性策略和参照点诱发的情绪波动会引发概率权重偏差; 改变“概率”的描述形式、“结果”的情绪体验、“损益”的参照点、风险的心理距离等可调整权重偏差、优化决策。未来需深究权重偏差的适用情境、机制关联及偏差辨别等问题。     

Contingency and choice: The implications of matching theory for classroom instruction

This paper describes a mathematical account of behavior known as matching theory. Matching theory evolved out of basic operant research and assumes that individuals can engage in a variety of behaviors at any moment, but they choose one to the exclusion of others. According to the matching equation, choices in behavior match the relative amount of reinforcement provided for each alternative. Although the principles of matching theory have proven useful in developing novel treatment strategies, few data exist validating the matching equation in natural human environments. Recent applications of matching theory to children's classroom behavior are described, and the implications of matching theory for classroom management and effective teaching are discussed.     

Probability matching in visual selective attention

Jonides (1980, p. 111) suggested a model to account for shifts of spatial attention in visual search tasks with less than 100% cue validity. This two-stage probability matching model was subsequently tested by Jonides (1983). Reaction time distribution characteristics indeed provided some support for the model. In the present paper the relevant data presented in Jonides (1980, 1981, 1983) are further analysed. The results of this analysis strongly support the probability matching hypothesis. Probability matching is apparently a very important strategic characteristic of visual spatial attention that deserves much more study.     

Probability matching in the right hemisphere

Previously it has been shown that the left hemisphere, but not the right, of split-brain patients tends to match the frequency of previous occurrences in probability-guessing paradigms (Wolford, Miller, & Gazzaniga, 2000). This phenomenon has been attributed to an "interpreter," a mechanism for making interpretations and forming hypotheses, thought to reside exclusively in the left hemisphere. In this study with a split-brain patient, we had him guess one of two types of faces, stimuli known to be preferentially processed in the right hemisphere of this patient. Unlike previous studies using other kinds of stimuli, the right hemisphere matched the frequency of the previous occurrences of a face-type, but the left hemisphere did not.     

Probability matching: encouraging optimal responding in humans.

Two hundred undergraduate students participated in a repeated-trials binary choice procedure in which choice of one outcome was correct on 75% of trials. Subjects received 192 trials and were divided into five conditions: (1) control; (2) subjects were given the actual probabilities; (3) subjects were told if they did well they could leave early; (4) competition condition; (5) midway through the task subjects were asked to recommend a strategy for another subject. Half of the subjects in each group were told that the best they could do was to be correct on 75% of the trials. This manipulation permitted assessment of the hypothesis that subjects in probability-matching tasks are seeking a strategy that will be correct on 100% of the trials. The results partially confirmed this hypothesis. In addition, two of the variables improved performance significantly (giving probabilities and asking subjects to recommend a strategy). However, while subjects in all groups improved significantly over trials, optimal choice did not occur in this task.     

Emotion regulation and risk taking: Predicting risky choice in deliberative decision making

Only very recently has research demonstrated that experimentally induced emotion regulation strategies (cognitive reappraisal and expressive suppression) affect risky choice (e.g., Heilman et al., 2010). However, it is unknown whether this effect also operates via habitual use of emotion regulation strategies in risky choice involving deliberative decision making. We investigated the role of habitual use of emotion regulation strategies in risky choice using the “cold” deliberative version of the Columbia Card Task (CCT; Figner et al., 2009). Fifty-three participants completed the Emotion Regulation Questionnaire (ERQ; Gross & John, 2003) and—one month later—the CCT and the PANAS. Greater habitual cognitive reappraisal use was related to increased risk taking, accompanied by decreased sensitivity to changes in probability and loss amount. Greater habitual expressive suppression use was related to decreased risk taking. The results show that habitual use of reappraisal and suppression strategies predict risk taking when decisions involve predominantly cognitive-deliberative processes.     

Goal attainment as a resource: The cushion effect in risky choice above a goal

Goals are a ubiquitous part of life and have been shown to change behavior in many domains. This research studied the influence of goal attainment on risky choice behavior. Previous research has shown that goals tend to increase risk‐seeking behavior when potential outcomes fall below a goal. We examined a new problem: Choice behavior when all potential outcomes in a choice set achieve or exceed the goal. Two studies show a “cushion effect” of goal attainment on choice under risk. When all possible outcomes of all options are above a salient and specific goal, decision makers are more likely to choose a risky option over a certain outcome with equal expected value (EV). We hypothesized that the attainment of a goal serves as a cushion that softens the negative emotions associated with receiving a gamble's low outcome. This allows risk taking that would otherwise be unattractive. Copyright © 2009 John Wiley & Sons, Ltd.